Non-linear viscous oscillatory flow over a small amplitude wavy wall

Abstract

The non-linear viscous oscillatory flow over a wavy wall of small amplitude ∊∗ is determined. The solution holds for arbitrary values of a ∗/L ∗ (a ∗ is the amplitude of fluid oscillations near the wall and L ∗ is the wavelength of wall perturbation); previous works of Lyne [1], Kaneko and Honji [2] on the subject are thus extended. An independent analysis for small values of a ∗/L ∗ is performed and the results of the two approaches have been successfully compared. The form of the steady streamings set up in addition to the oscillatory motion by the bed profile is analyzed for different values of the parameters of the problem. The relevance of the results to the study of ripples formation at the bottom of sea waves is discussed.